Q. $\int_{- 1/7}^{20/7}{\sin{\left( x - \lbrack x\rbrack \right)dx}}$ (where $\lbrack \bullet \rbrack$ denotes greatest integer) is
A) 0
B) $3\ (\cos{1 - 1)}$
C) $3(1 - \cos{1)}$
D) None of these
Explanation
(c)
$I = \int_{- 1/7}^{20/7}{\sin{\left( x - \lbrack x\rbrack \right)dx = \int_{- 1/7}^{3 - \frac{1}{7}}{\sin{\left( \left\{ x \right\} \right)dx}}}}$
$= 3\int_{0}^{1}{{\sin{x\ dx = 3\lbrack - \cos{x\rbrack}}}_{0}^{1} = 3(1 - \cos{1)}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.